\(\mathrm {QuaNT}\)  is a learning algorithm that constructs a PDFA by interacting with a teacher which makes use of oracles \(\mathbf {MQ}_{\mathrm {QuaNT}}\)  and \(\mathbf {EQ}_{\mathrm {QuaNT}}\) . It has three major differences with \(\mathrm {WL}^\ast \) .
First, \(\mathbf {MQ}_{\mathrm {QuaNT}}\)  returns the next-symbol probability simplex of a string, that is \(\mathbf {MQ}_{\mathrm {QuaNT}}(s) = \pi ^\ast (s)\)  for \(s\in \Sigma ^\ast \) ; while \(\mathbf {MQ}_{\mathrm {WL}^\ast }(s)\)  returns \(\pi ^\ell _{q_{\mathrm {in}}}(s)\) , where \(\pi ^\ell \)  is defined in (REF ).
Second, it relies on quantization rather than on tolerance for comparing probability distributions. Since our quantization method induces a congruence, there is no need for clustering states.
Third, along the lines of [1]} and  [2]} algorithms, \(\mathrm {QuaNT}\)  builds a classification tree instead of a table. Similarly to these algorithms, tree leafs are PDFA states identified by so-called access strings and inner nodes are distinguishing suffixes. Nevertheless, in \(\mathrm {QuaNT}\)   the tree is not binary but \(n\) -ary, where \(n\)  is the number of different classes which \(\Delta (\Sigma _\$)\)  is partitioned into, and tree arcs and leafs are labelled with elements of \(\left<\Delta (\Sigma _\$)\right>_\kappa \)  and \(\Delta (\Sigma _\$)\) , respectively.
